# MATH PROJECT COMIC STRIP

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#### Storyboard Text

• ln derivative f (x) = ln(x) ⇒ f ' (x) = 1 / x d/dx (a^x) = a^x ln a U substitution ∫du/u = ln | u | + c In integral ∫ ln(x)dx = x ∙ (ln(x) - 1) + c
• LET'S DO SOME MATH GUYS! ﻿For u substitution, you would take the whole thing before the dx and call that u and then would derive it to get du
• ﻿and remember if you get to ∫e^u du you know that the integral of e^u is e^u + C and don't forget to plug back in u into the integral.
• ﻿if du is in the integral solve, but if it isn't you would need some math makeup. solve and then use the Voldemort's line for your limits if it is a definite integral.
• so if it was ∫5/2x dx, it would = 5/2 ln x +c. also the position of du and u matters when you integrate it
• ﻿so if you have f(x)= ln (x+5)/(x-1) you can go either the hard way or the easy way. You can decipher that you can use your properties to put it as ln a - ln b, or use the chain rule which takes forever and can potentially cause errors. you get the same answer as f'(x)= 1/x+5 - 1/x-1, now do this practice quiz...
• ﻿20 HOURS LATER......
• GOOD MORNING MR. ROLLO-KOSTER
• GOOD MORNING CLASS
• WHO IS READY FOR THIS TEST?
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